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Kernel estimators of mode under $$\psi $$ ψ -weak dependence

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  • Eunju Hwang
  • Dong Shin

Abstract

Nonparametric kernel-type estimation is discussed for modes which maximize nonparametric kernel-type density estimators. The discussion is made under a weak dependence condition which unifies weak dependence conditions such as mixing, association, Gaussian sequences and Bernoulli shifts. Consistency and asymptotic normality are established for the mode estimator as well as for kernel estimators of density derivatives. The convergence rate of the mode estimator is given in terms of the bandwidth. An optimal bandwidth selection procedure is proposed for mode estimation. A Monte-Carlo experiment shows that the proposed bandwidth yields a substantially better mode estimator than the common bandwidths optimized for density estimation. Modes of log returns of Dow Jones index and foreign exchange rates of US Dollar relative to Euro are investigated in terms of asymmetry. Copyright The Institute of Statistical Mathematics, Tokyo 2016

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  • Eunju Hwang & Dong Shin, 2016. "Kernel estimators of mode under $$\psi $$ ψ -weak dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 301-327, April.
    • Handle: RePEc:spr:aistmt:v:68:y:2016:i:2:p:301-327
    DOI: 10.1007/s10463-014-0489-2
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    References listed on IDEAS

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    1. Roussas, George G., 1990. "Nonparametric regression estimation under mixing conditions," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 107-116, October.
    2. Frédéric Ferraty & Ali Laksaci & Philippe Vieu, 2006. "Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models," Statistical Inference for Stochastic Processes, Springer, vol. 9(1), pages 47-76, May.
    3. Vieu, Philippe, 1996. "A note on density mode estimation," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 297-307, March.
    4. Herrmann, Eva & Ziegler, Klaus, 2004. "Rates of consistency for nonparametric estimation of the mode in absence of smoothness assumptions," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 359-368, July.
    5. Shi, Xiaoping & Wu, Yuehua & Miao, Baiqi, 2009. "Strong convergence rate of estimators of change point and its application," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 990-998, February.
    6. Shi, Xiaoping & Wu, Yuehua & Miao, Baiqi, 2009. "A note on the convergence rate of the kernel density estimator of the mode," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1866-1871, September.
    7. Hwang, Eunju & Shin, Dong Wan, 2012. "Stationary bootstrap for kernel density estimators under ψ-weak dependence," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1581-1593.
    8. Nze, Patrick Ango & Doukhan, Paul, 2004. "Weak Dependence: Models And Applications To Econometrics," Econometric Theory, Cambridge University Press, vol. 20(6), pages 995-1045, December.
    9. Doukhan, Paul & Neumann, Michael H., 2007. "Probability and moment inequalities for sums of weakly dependent random variables, with applications," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 878-903, July.
    10. Coulon-Prieur, Clémentine & Doukhan, Paul, 2000. "A triangular central limit theorem under a new weak dependence condition," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 61-68, March.
    11. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    12. Paul Doukhan & Sana Louhichi, 2001. "Functional Estimation of a Density Under a New Weak Dependence Condition," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(2), pages 325-341, June.
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